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<p>This study proposes an iterative approach for solving nonlinear general quadratic Riccati differential equations. The proposed method integrates the Daftardar-Gejji and Jafari Method (DGJM) with the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>-method family. We analyze convergence, stability, and error estimates using the Lipschitz condition and Taylor series expansion to investigate its performance. Numerical results are compared with the exact solution and the Runge–Kutta family of methods, demonstrating that the proposed scheme is highly accurate and efficient. Moreover, the suggested approach can be easily implemented using computer algebra systems such as Mathematica, Maple, and MATLAB.</p>

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An Iterative Technique Based on Daftardar-Gejji and Jafari Method for Solving the General Quadratic Riccati Differential Equations

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Amit Prakash,
  • Manoj Kumar

摘要

This study proposes an iterative approach for solving nonlinear general quadratic Riccati differential equations. The proposed method integrates the Daftardar-Gejji and Jafari Method (DGJM) with the \(\theta \) θ -method family. We analyze convergence, stability, and error estimates using the Lipschitz condition and Taylor series expansion to investigate its performance. Numerical results are compared with the exact solution and the Runge–Kutta family of methods, demonstrating that the proposed scheme is highly accurate and efficient. Moreover, the suggested approach can be easily implemented using computer algebra systems such as Mathematica, Maple, and MATLAB.